Despite being a native speaker of American English, I cannot find a construction that sounds natural when trying to form a possessive from coordinated subjects including a first person pronoun, like "He and I" or "My brother and I." If it's "You and I," I can just use "our." But what is the proper way to form a possessive in these other instances?

The cat which belongs to my brother and me ran away.

? My brother and I's cat ran away.

* My brother's and my cat ran away.

*/? Me and my brother's cat ran away.

Oddly enough, the one which sounds the most natural to me (and which I hear most often in natural speech, is the last: "me and my brother's." My hypothesis is that this is used to avoid the issue with the first-person possessive form, but that could very well be wrong.

However, I'm not sure this is the best answer, either, as it introduces some pretty bad ambiguity in some places.

A person who is a friend to both my brother and me got married yesterday.

*/? Me and my brother's friend got married yesterday.

I think you can see the obvious problem.

What is the proper way to possessivize coordinated first-/third-person subjects?

Edit: I would much prefer an answer which does not require rephrasing the entire sentence.

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

The short answer (correctly expanded by @Thursagen) is that there is no answer which does not require extensive rephrasing of the entire sentence. There's inherent ambiguity in the scope of the possessive 's, and no trivial tweak will get around this if the context doesn't do it for you.
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FumbleFingersAug 22 '11 at 21:09

1

This is such a great question I'm seriously thinking about offering a bounty from my own reputation for the best answer ...
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RiMMERAug 23 '11 at 15:37

Doesn't sound quite right but there's no law against using "I's".
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user37949Feb 20 '13 at 12:28

@user37949 I've recently come to this conclusion as well, and despite sounding odd, I believe it is the proper grammatical answer.
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rintaunMar 7 '13 at 20:49

+1 Despite the fact that it sounds awkward, your construction "Shelby's and my" --> "My brother's and my friend got married yesterday" seems to me to be the best way to avoid ambiguity without having to rephrase the sentence; unfortunately, ambiguity remains when this sentence is spoken... Perhaps "My and my brother's friend..."? As for what is "incorrect", see english.stackexchange.com/questions/4226/…
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nxxMar 23 '14 at 18:03

You can still use our as long as you are one of the people in that group. That is, you and I, he and I, Billy, Joe, and I can all use the pronoun our in order to describe the possessive.

If you want to form the more complex possessive to show joint ownership, this site explains:

When a sentence indicates joint ownership in a compound construction, the possessive form is attached only to the second noun:

Deanna and Brandi's vacation plans

Tim and Bethany's wedding invitation

Note that individual ownership is marked by a double possessive:

Courtney's and Mem's grade point averages

Tim and Bethany share the same wedding invitation, whereas Courtney and Mem each have their own grade point averages.

If the cat belonged to Joe and your brother, you would say:

Joe and my brother's cat ran away.

That is, you could answer "whose cat ran away?" with either "Joe's cat" or "my brother's cat". This could possibly be misconstrued to the effect that Joe and your brother's cat ran away together, however. In order to counteract this, despite it being the correct possessive, you can "cheat" and use:

Joe's and my brother's cat ran away.

Since there is only one cat, it implies that they both own it.

Since the cat belonged to you and your brother, then you would say:

My and my brother's cat ran away.

You would use my here because you can answer "whose cat ran away?" with "my cat". This formulation also solves your issue regarding the marriage example--if you say:

It is tricky to say something like this, and we generally end up puzzling over "My brother and I's"? The fact is, we want to state that the thing has joint ownership, and this is difficult to do so when one of the owners is yourself, due to the fact that "I", when replaced with "my", the normal possessive form, means a different thing:

My brother's and my cat

implies that there are two cats.

In order to effectively state that the cat belongs to both you and your brother, and that there is only one cat, I would suggest an alternative:

The cat which belonged to my brother and I.
The cat of my brother and I.